5. Graphical Applications of Derivatives

75. b. Identify the function’s local and absolute extreme values, if any, saying where they occur.

g(x) = x(ln x)²

133. Find the absolute maximum value of

f(x) = x^2 * ln(1/x)

and say where it is assumed.

In Exercises 115 and 116, find the absolute maximum and minimum values of each function on the given interval.

116. y = 10x (2 - ln(x)), (0, e²]"133. Find the absolute maximum value of

f(x) = x^2 * ln(1/x)

and say where it is assumed

130. Where does the periodic function f(x) = 2e^(sin(x/2)) take on its extreme values, and what are these values?